10. What is the volume, in cu. yds., of a rectangular piece of masonry 4 yd. 1 ft. 6 in. long, 3 yd. 2 ft. 3 in. wide, 2 yd. 1 ft. high?

11. How many boards, each having a surface of 7 sq. ft. 60 sq. in., are equal in area to a surface measuring 37 sq. yd. 108 sq. in.

SUGGESTION. Reduce each quantity to sq. in.

12. How many tiles, each having a surface 5

sq. in., will cover the floor of a hall 173 sq. ft. 48 sq. in. in area? 13. Into how many pieces, each containing 1 sq. ft. 36 sq. in., may a roll of paper measuring 13 sq. yd. 8 sq. ft. be cut?

SOME PRACTICAL RULES.

343. The following practical rules are used by builders and others for rapid computation. The results are only approximately correct, but sufficiently accurate for estimates.

344. Lathing. A lath is 4 ft. long, and usually 1 in. or 13 in. wide. There are 50 laths in a bundle. In making estimates, contractors usually deduct one half of the area of openings for doors and windows, and adopt this rule :

One bundle of lath will cover 3 square yards.

1. How many bundles of lath are needed to cover a ceiling 15 ft. by 21 ft. ?

2. How many bundles of lath are needed for the walls of a room 18 ft. long, 15 ft. wide, 10 ft. high, making the usual deduction for 3 doors, each 23 ft. by 7 ft., and 4 windows, each 2 ft. by 6 ft. ?

3. How many bundles of lath are needed for the walls

and ceiling of a room 16 ft. wide by 28 ft. long, 9 ft.

high, with 2 doors, each 7 ft. by 6 ft., and 8 windows,

each 3 ft. by 6 ft.?

SUGGESTION. When a room is 9 ft. high, the number of sq. yards in its walls is equal to the number of feet in its perimeter.

345. Shingling. Shingles are considered as averaging 4 in. in width. A bunch contains 250 shingles. With due allowance for waste, the usual rule is :

Laid 4 inches to the weather, 1000 shingles will cover 100 square feet.

1. How many bunches of shingles, laid 4 in. to the weather, will cover the roof, each half of which is 40 ft. by 20 ft.?

NOTE.

Dealers do not sell less than a bunch. The result should contain no fractions.

2. A double roof is 54 ft. long; the rafters are 24 ft. long. Find cost of necessary shingles, at $3.75 per M. 346. Flooring and Siding. To find the number of sq. ft. of matched lumber to cover a given area:

I. For 6 inch matched lumber, find six fifths of the number of sq. ft. to be covered.

II. For 3 inch matched lumber, find four thirds of the number of sq. ft. to be covered.

1. How many sq. ft. of 6 in. matched lumber are needed to cover a floor 56 ft. by 30 ft.?

2. Find cost of siding, with 6 in. matched lumber, the walls of a house 60 ft. long by 36 ft. wide by 24 ft. high, the lumber costing $22 per M.

3. Find cost of 3 in. matched flooring, at $38 per M., sufficient to floor 6 rooms, each 15 ft. by 21 ft.

347. Board Measure. Sawed lumber is generally sold by Board Measure. A board foot is the measure of a board 1 foot long, 1 foot wide, 1 inch thick.

A board 12 ft. long, 1 ft. wide, 1 in. thick, contains 12

ft. board measure.

12 ft. 24 ft. If 1

If 2 inches thick, it contains 2×

inches thick, it contains 1×12

ft. 18 ft. board measure.

A board less than 1 inch thick is considered as measur-
ing the same as if it were 1 inch thick. Thus, a board
12 ft. long, 1 ft. wide, in. thick, contains 12 board
feet.

To find the number of board feet in sawed lumber:
Multiply the length of the piece by its width, both expressed

in feet; then multiply this product by its thickness expressed in inches, if the thickness is 1 inch or more. 1. How many feet board measure in 60 boards, each 16 ft. long, 9 inches wide, in. thick ?

2. How many feet board measure in 40 planks, each 12 ft. long, 14 in. wide, 13 in. thick ?

3. How many feet board measure in 36 joists, each 18 ft. long, 10 in. wide, 2 in. thick ?

4. Find cost, at $40 per M., of 12 scantling, each 24 ft. long, by 8 in. by 8 in.

348. Stone Masonry. To find the number of perches of stone masonry:

Divide the number of cubic feet by 25.

1. How many perches of masonry in an abutment 20 ft. wide, 15 ft. thick, 35 ft. high?

349. Brickwork. To find the number of bricks laid in a wall: Multiply the number of cubic feet in the wall by 221.

1. How many bricks in a wall 80 ft. by 10 ft. by 21⁄2 ft. ? 2. How many bricks necessary for the 12 inch walls of a house 48 ft. long, 24 ft. wide, 22 ft. high, deducting 56 cu. ft. for openings?

350. To Find the Number of Gallons in a Cistern.

1728 (the no. of cu. in. in a cu. ft.)÷231 (the no. of

cu. in. in a gal.)=7.48, which is nearly 7. Hence, Multiply the number of cu. feet in the bin by 71.

1. How many gallons in a cistern 7 ft. deep, the base of
which has an area of 38 sq. ft.?

2. How many gallons in a tank 6 ft. by 8 ft. by 4 ft. ?
3. How many gallons in a tub having a base of 4 sq. ft.,
and a depth of 15 inches?

4. How many gallons in a bucket having a base of 72
sq. in., and a depth of 12 inches?

351. To Find the Number of Bushels in a Bin.

1728÷2150.4 (the number of cu. in. in a bush.) = nearly.
Hence,

Take four fifths of the number of cubic feet in the bin.
1. How many bushels in a bin whose cubical contents are
9250 cu. ft.?

2. How many bushels in a bin which is 20 ft by 10 ft.
by 6 ft.?

3. How many cu. ft. will be occupied by 3416 bushels of grain?

4. How many cu. ft. are necessary to store 2596 bushels of grain?

352. To Measure Coal. A ton (2000 lbs.) of anthracite coal (Lehigh, range) measures about 34 cu. ft.; a ton (2000 lbs.) of bituminous coal measures about 41 cu. ft. 1. How many tons of anthracite coal in a bin 8 ft. by 81 ft. by 4 ft?

2. How many tons of bituminous coal in a bin 104 ft. by 5 ft. by 3 ft ?

3. How many cu. ft. in a bin holding 5,3 tons of anthracite

coal ? In one holding 72 tons of bituminous coal ? 4. How many cu. ft. in the bunkers of a steam vessel that uses 122 tons of bituminous coal a day, and carries enough coal to last 8 days?

СНАРТER XII.

PERCENTAGE.

Article 353. 1. A farmer gave to the poor 6 bushels out of every 100 bushels of grain which he raised. How many bushels did he give when his crop was 500 bushels ? When it was 800 bushels ?

How many hnndredths of his grain did he give to the poor? 2. A student spends for books $12 of every $100 of his

income. How many hundredths of his income does he spend for books? How many dollars does he spend for books when his income is $600?

3. A fruit grower who had 400 trees, lost 8 out of every hundred of them. How many trees did he lose? How many hundredths of his trees did he lose?

4. A farmer who had 50 trees lost 10 hundredths of them. How many trees did he lose? At the same rate, how many would he have lost if he had had 100 trees? 200 ? 300 ? Would he have lost in each case, the same number of hundredths ?

Instead of saying, as in example 3, "8 out of every hundred," or, "8 hundredths," we say "8 per cent." Therefore,

354. Per cent means hundredths.

1 per cent is 100; 6 per cent is 6 hundredths, etc.

Instead of the words "per cent," the sign % is frequently used.

355. Rate per cent means a certain number of hundredths. In the expression 6 per cent, 6 is the rate. The rate is the numerator of a fraction of which the denominator is always 100.